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  • Articles  (2)
  • Key words. Capillary-gravity waves, third harmonic resonance, multiple scales, evolution equation.  (1)
  • Key words. Capillary-gravity, mode interaction, O(2)-invariance, bifurcation, Lyapunov-Schmidt, universal unfolding.  (1)
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  • Articles  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    A codimension seven unfolding of a third harmonic resonant interaction between two contiguous continua (2000)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 51 (2000), S. 651-673 
    Details
    ISSN: 0044-2275
    Keywords: Key words. Capillary-gravity, mode interaction, O(2)-invariance, bifurcation, Lyapunov-Schmidt, universal unfolding.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. In this paper we study the capillary-gravity profiles which may occur at the interface of two fluids when the fundamental mode and its third harmonic interact with each other. The problem is treated as one in bifurcation theory by transforming it into a nonlinear operator equation between suitable function spaces. Using classical analytic methods and by exploiting the group invariances of the operator, we are able to describe the solution set of the equation for a selection of values of the parameters present and to allow for possible imperfections in the resonance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00001513
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A nonlinear multiple scales approach to modelling almost third harmonic interfaces (1999)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 50 (1999), S. 47-63 
    Details
    ISSN: 0044-2275
    Keywords: Key words. Capillary-gravity waves, third harmonic resonance, multiple scales, evolution equation.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. The evolution of third harmonic resonant narrow bandwidth capillary–gravity waves on an interface of two fluids is considered. The method of multiple scales is utilised in order to derive a set of first order coupled nonlinear partial differential equations which model the evolution of the wavepacket. Some solution families are exhibited.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000330050138
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    Paper (German National Licenses)
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